Script for generating some cool collatz plot.

collatz.py

from matplotlib import pyplot as plt

class Node(object):
    def __init__(self, num, step, parent, children):
        self.num = num
        self.step = step
        self.parent = parent
        self.children = children

class Collatz(object):

    def __init__(self):
        self.memo = {}
        self.memo['nums_at_step'] = {0: [1]}
        self.memo['step_for_num'] = {}

    def get_step(self, n):
        step = 0
        while n > 1:
            if n % 2 == 0:
                n /= 2
            else:
                n = (3*n) + 1
            step += 1
        return step

    def get_nums(self, s):
        if s in self.memo['nums_at_step']:
            return self.memo['nums_at_step'][s]
        previous_nums = self.memo['nums_at_step'][s-1]
        new_nums = []
        for num in previous_nums:
            new_nums.append(num * 2)
            if (num - 1) % 3 == 0 and (num - 1) / 3 > 1:
                new_nums.append((num-1)/3)
        new_nums = [x for x in set(new_nums) if x < 10000]
        print s, new_nums
        self.memo['nums_at_step'][s] = new_nums
        return new_nums

c = Collatz()

plt.figure(1, figsize=(16, 12))
plt.subplot(111)
xmax = 100000
x = [i for i in xrange(xmax)]
y = [c.get_step(i) for i in x]
plt.scatter(x,y)
plt.ylim(ymin=0)
plt.xlim([0,xmax])
plt.savefig('c.png')